Abstract

A number of recent studies have shown that mechanical stress can significantly lower or raise the activation barrier of a chemical reaction. Within a common approximation due to Bell [Science200, 618 (1978)], this barrier is linearly dependent on the applied force. A simple extension of Bell's theory that includes higher order corrections in the force predicts that the force-induced change in the activation energy will be given by –FΔR – ΔχF2/2. Here, ΔR is the change of the distance between the atoms, at which the force F is applied, from the reactant to the transition state, and Δχ is the corresponding change in the mechanical compliance of the molecule. Application of this formula to the electrocyclic ring-opening of cis and trans 1,2-dimethylbenzocyclobutene shows that this extension of Bell's theory essentially recovers the force dependence of the barrier, while the original Bell formula exhibits significant errors. Because the extended Bell theory avoids explicit inclusion of the mechanical stress or strain in electronic structure calculations, it allows a computationally efficient characterization of the effect of mechanical forces on chemical processes. That is, the mechanical susceptibility of any reaction pathway is described in terms of two parameters, ΔR and Δχ, both readily computable at zero force.

Received 25 August 2011Accepted 07 October 2011Published online 27 October 2011

Acknowledgments:

We acknowledge support from the Army Research Office (Grant No. W911NF-07-10409), the Robert A. Welch Foundation (Grants Nos. F-1621 and F-1514), and the National Science Foundation (Grant No. CHE 0848571). Computational resources were provided by the Texas Advanced Computing Center.